Rotationally stretch or compress 3D texture around Z axis
Found it.
The idea is to use a gradient node in radial mode and plug it to the angle of a rotation node (just like a Mapping node but with an input socket for the rotation). Since such a node doesn't exist in Blender we make it with math nodes.

First the rotation node itself (it's a node group) :



then the general setup (the green node is the rotation we made above and the yellow node is the one to animate (the second value in the Multiply node) :



Result : 



Here is the file :